Problem 3:

Consider the following information on three securities.

Table (panel A)

SecurityE(return)Variance () Beta ()

A.1135.04841.15

B.05.0625.25

C.0775.0225.75

Correlations are shown in the following table; e.g., the entry in the B row and C column is the correlation coefficient between B and C.

Table (panel B)

ABC

A1.00.169.847

B.1691.00.162

C.847.1621.00

A fourth security is risk-free Treasury STRIPS (i.e., zero coupon bonds) that mature in exactly one year with an effective annualized yield of 1%.The return on a board-based portfolio (i.e., the market) is expected to be .10 (10%) over the next year; its standard deviation is .18 (18%).

Questions:

1.Based on the information provided above, what should be the expected returns for A, B, and C according to CAPM?If you believe CAPM is correct, which securities do you want to favor and which securities do you want to shy away from?

2.If you form a portfolio using $10,000 invested in A and $10,000 invested in B (i.e., a portfolio with 50% in A and 50% in B), what is the expected return on that portfolio given the data above?Recall that the expected return of a portfolio is simply the weighted average of the expected returns of the individual securities in the portfolio (in this case, A and B), where the weights are the fraction of the total money invested that is invested in each individual security (in the case the weighs are both .5 or 50%).It is also the case the beta of the return on a portfolio is simply the weighted average of the betas of the individual securities in the portfolio, again with weights that are the fraction of the total invested money invested in each security.What is the beta of that portfolio? Using the beta of the portfolio, what does CAPM imply the expected return on the portfolio should be?How does that compare to that predicted by the data above?

3.What portfolio of A and B will give you a portfolio that has the same beta as security C?That is, solve for the weight on A (denoted w_A) and (1-w_A) on B such that the portfolio beta is .75.That is, solve for w_A such that

w_A*1.15 + (1-w_A)*.25 = .75.

What is the expected return on this portfolio using the data in the table above?How does that compare to the expected return for security C shown in the table?If they are different, you should "short" the one with the low expected return (by "shorting" you borrow the security and sell it - you will have to buy it back later, after it has on average increase by its expected return; thus, shorting a security is similar to borrowing money at the securities expected return) and use the proceeds to buy (i.e., invest in) the one with the high expected return.By doing so, you earn the spread between the two rates, without having to invest any of your own money.

4.Consider what happens to prices and returns if you (and a bunch of other people) execute the strategy you identified above.Given the pressure on prices given the above trades, will the expected returns on the various securities move in a direction that makes them more consistent with CAPM or less consistent with CAPM?